Penalized empirical likelihood based variable selection

TL;DR: The approach to variable selection in Cox’s proportional hazard model is extended, and the asymptotic properties of the new penalized-empirical-likelihood method are investigated, and an algorithm for estimating the parameters are developed.

Abstract: Variable selection is an important topic in high-dimensional statistical modeling, especially in generalized linear models Several variable selection procedures have been developed in the literature, including the sequential approach, prediction-error approach, and information-theoretic approach All of these are computationally expensive A new method based on penalized likelihood has been lauded for its computational efficiency and stability In this approach the variable selection and the estimation of the coefficients are carried out simultaneously The parametric likelihood is a crucial component, but in many situations a well-defined parametric likelihood is not easy to construct To overcome this problem, Variyath (2006) proposed a penalized-empirical-likelihood (PEL) based variable selection where empirical likelihood is constructed based on a set of estimating equations We investigate the asymptotic properties of the new method, and develop an algorithm for estimating the parameters Our simulation studies show that when a parametric model is available, PEL-based variable selection gives results similar to those achieved by parametric-likelihood variable selection The former method outperforms the latter when the parametric model is misspecified We extend our approach to variable selection in Cox’s proportional hazard model